In the figure the diameter of the circle is 20 cm. Two A
parallel chords are drawn in the circle. They are
AB = 16 cm and CD= 12 cm. Find the distance between
these chords.
M
T
1
10
CN=
cm
BM =
C С
D
cm
OC =
cm
OB =
cm
Write the distance from the centre of the circle to the chord AB.
Write the distance from the centre of the circle to the chord CD.
II
Write the distance between the chords.
If the chords are drawn on the same side of the centre, then
What is the distance between them?
Answers
Answer :
AB=16cm
AM=MB=8cm
CD=12 cm
CN=ND=6 cm
diameter =20 cm i. e. Radius=10 cm
CO=OB=10 cm
Angle ONC is 90°
i. e. ONC is a right angle triangle
(CO)^2 =(ON)^2 +(CN)^2 (by Pythagoras theorem)
10^2 =(ON)^2 +6^2
100 =(ON)^2 +36
100-36=(ON)^2
64=(ON)^2
ON=8 cm
Angle OMB is 90°
i. e. OMB is a right angle triangle
(OB)^2 =(OM)^2 +(MB)^2 (by Pythagoras theorem)
(10)^2 =(OM)^2 + 8^2
100=(OM)^2 +64
100-64=(OM)^2
36=(OM)^2
OM =6 cm
The distance between the chords are (6+8) cm = 14 cm
the distance from the centre of the circle to the chord AB is 6 cm
the distance from the centre of the circle to the chord CD is 8 cm
If the chords are drawn on the same side of the centre, then the distance between the two chords are (8-6)cm=2cm
Given : The diameter of the circle is 20cm.
Two parallel chords are drawn in the circle.
AB =16cm and CD=12cm
To Find : distance from the centre of the circle to the chord AB.
distance from the centre of the circle to the chord CD.
distance between the chords.
If the chords are drawn on the same side of the centre, then distance between chords
Solution:
Perpendicular from the center of the circle bisects the chord
Hence CN = CD/ 2
=> CN = 12/2
=> CN = 6 cm
Diameter = 20 cm => Radius = 10 cm
CN = 6 cm
=> ON = √10² - 6² = 8 cm
M is mid point of AB
=> AM = 8 cm
and OM = √10² - 8² = 6 cm
Distance between chords AB and CD = 8 + 6 = 14 cm
distance from the centre of the circle to the chord AB. = 6 cm
distance from the centre of the circle to the chord CD. = 8 cm
distance between the chords. = 14 cm
If the chords are drawn on the same side of the centre, then distance between chords = 8 - 6 = 2 cm
Learn More:
Radius of a circle is 10 cm and length of one of its chords is 12 cm ...
brainly.in/question/7145159
pq is a chord of length 8 cm of a circle of radius 5cm - Brainly.in
brainly.in/question/3055481
pq is a chord of length 8 cm of a circle of radius 5cm - Brainly.in
brainly.in/question/3055481